Question

As a preparation for the long bright summer days, Dr. Acula plans to store gourmet plasma in closed tin cans that have the shape of a cylinder with volume 450 cm³. As an environmentally conscious member of the community, he wants to use as little metal as possible. What is the minimum amount of metal required to make a closed tin can with a volume of 450 cm³?

Answer 1

To find the minimum amount of metal required to make a closed tin can with a volume of 450 cm³, we need to calculate the surface area of the can and minimize it.

Step-by-step explanation:

To find the minimum amount of metal required to make a closed tin can with a volume of 450 cm³, we need to calculate the surface area of the can. The surface area of a cylinder can be calculated using the formula:

Surface Area = 2πrh + 2πr²

Since we want to use as little metal as possible, we need to minimize the surface area. To do this, we can take the derivative of the surface area formula with respect to r, set it equal to 0, and solve for r. This will give us the radius that minimizes the surface area. Once we have the radius, we can substitute it back into the surface area formula to find the minimum surface area.